Wednesday evening finish five pole LP filter

analysis

opamp_circuits_C_GARRETT/opamps.tex

@@ -464,7 +464,7 @@ wihen it becomes a V2 follower).
  \centering
  \includegraphics[width=200pt]{./circuit2002.png}
  % circuit2002.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331
- \caption{circuit2}
+ \caption{circuit 2}
  \label{fig:circuit2}
 \end{figure}
 
@@ -478,6 +478,16 @@ The output of this is passed into another Sallen~Key filter (which although it m
 for its resistors/capacitors and thus a different frequency response) is idential from a failure mode perspective.
 Thus we can analyse the first Sallen~Key low pass filter and re-use the results.
 
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=400pt,keepaspectratio=true]{./blockdiagramcircuit2.png}
+ % blockdiagramcircuit2.png: 689x83 pixel, 72dpi, 24.31x2.93 cm, bb=0 0 689 83
+ \caption{Signal Flow though the five pole low pass filter}
+ \label{fig:blockdiagramcircuit2}
+\end{figure}
+
+
 \paragraph{First Order Low Pass Filter.}
 We begin with the first order low pass filter formed by $R10$ and $C10$.
 %
@@ -504,9 +514,11 @@ We will consider the latter type for this analysis.
                \hline
      FS1: R10 SHORT    &  &  $No Filtering$   &  &    $LPnofilter$           \\ \hline
      FS2: R10 OPEN     &  &  $No Signal$      &  &    $LPnosignal$           \\ \hline
-     FS3: C10 SHORT    &  &  $No Signal$      &  &    $LPnosignal$         \\ \hline
+     FS3: C10 SHORT    &  &  $No Signal$      &  &    $LPnosignal$           \\ \hline
-     FS4: C10 OPEN     &  &  $No Filtering$   &  &    $LPnofilter$            \\ \hline
+     FS4: C10 OPEN     &  &  $No Filtering$   &  &    $LPnofilter$           \\ \hline
+
 \hline
+
 \end{tabular}
 \end{table}
 
@@ -527,17 +539,17 @@ from the $FirstOrderLP$ and the OPAMP component.
 \centering % used for centering table
 \begin{tabular}{||l|c|c|l|l||}
 \hline \hline
- \textbf{Test} & \textbf{Amplifier} & \textbf{  } & \textbf{General}   \\
+ \textbf{Test} & \textbf{Circuit} & \textbf{  } & \textbf{General}   \\
  \textbf{Case} &  \textbf{Effect}   & \textbf{  } & \textbf{Symptom Description}   \\
 %   R         &    wire        & res +         & res -    & description
 \hline
 \hline
  TC1: $OPAMP$ LatchUP      &  Output High                     &      &  LP1High \\ 
- TC2: $OPAMP$ LatchDown    &  Output Low                      &      &  LP1Low \\ \hline
+ TC2: $OPAMP$ LatchDown    &  Output Low                      &      &  LP1Low \\  
  TC3: $OPAMP$ No Operation &  Output Low                      &      &  LP1Low \\  
- TC4: $OPAMP$ Low Slew     &  Unwanted Low pass filtering     &      &  LP1ExtraLowPass \\ \hline
+ TC4: $OPAMP$ Low Slew     &  Unwanted Low pass filtering     &      &  LP1filterincorrect \\ \hline
- TC5: $LPnofilter $        &  No low  pass filtering          &      &  LP1NoLowPass \\ \hline
+ TC5: $LPnofilter $        &  No low  pass filtering          &      &  LP1filterincorrect \\ 
- TC6: $LPnosignal $        &  No input signal                 &      &  LP1low \\  
+ TC6: $LPnosignal $        &  No input signal                 &      &  LP1nosignal \\  \hline
                            \hline 
  
 \hline
@@ -549,7 +561,20 @@ From the table~\ref{tbl:firststage} we can see three symptoms of failure of
 the first stage of this circuit (i.e. R10,C10,IC1).
 We can create a derived component for it, lets call it $LP1$.
 
-$$ fm(LP1) = \{ LP1High,  LP1Low,  LP1ExtraLowPass, LP1NoLowPass \} $$
+$$ fm(LP1) = \{ LP1High,  LP1Low,  LP1filterincorrect, LP1nosignal \} $$
+
+
+In terms terms of the circuit we have modelled the functional groups $FirstOrderLP$, and 
+$LP1$. We can represent these on the circuit diagram by drawing contours around the components
+on the schematic as in figure~\ref{fig:circuit2002_LP1}.
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,keepaspectratio=true]{./circuit2002_LP1.png}
+ % circuit2002_LP1.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331
+ \caption{Circuit showing functional groups modelled so far.}
+ \label{fig:circuit2002_LP1}
+\end{figure}
 
 
 \paragraph{Second order Sallen Key Low Pass Filter.}
@@ -562,27 +587,30 @@ We can analyse one and re-use the results for the second.
 \centering % used for centering table
 \begin{tabular}{||l|c|c|l|l||}
 \hline \hline
- \textbf{Test} & \textbf{Amplifier} & \textbf{  } & \textbf{General}   \\
+ \textbf{Test} & \textbf{Circuit} & \textbf{  } & \textbf{General}   \\
  \textbf{Case} &  \textbf{Effect}   & \textbf{  } & \textbf{Symptom Description}   \\
 %   R         &    wire        & res +         & res -    & description
 \hline
 \hline
  TC1: $OPAMP$ LatchUP      &  Output High                     &      &  SKLPHigh \\ 
- TC2: $OPAMP$ LatchDown    &  Output Low                      &      &  SKLPLow \\ \hline
+ TC2: $OPAMP$ LatchDown    &  Output Low                      &      &  SKLPLow \\  
  TC3: $OPAMP$ No Operation &  Output Low                      &      &  SKLPLow \\  
- TC4: $OPAMP$ Low Slew     &  Unwanted Low pass filtering     &      &  SKLPIncorrect \\ \hline
+ TC4: $OPAMP$ Low Slew     &  Unwanted Low pass filtering     &      &  SKLPfilterIncorrect \\ \hline
- TC5: $R1 OPEN$            &  No input signal                 &      &  SKLPIncorrect                   \\ \hline
+ TC5: R1 OPEN            &  No input signal                 &      &  SKLPfilterIncorrect                   \\  
- TC6: $R1 SHORT$           &  incorrect low pass filtering    &      &  SKLPIncorrect                   \\  
+ TC6: R1 SHORT           &  incorrect low pass filtering    &      &  SKLPfilterIncorrect                   \\  \hline
- TC7: $R2 OPEN$            &  No input signal                 &      &  SKLPnosignal                  \\ \hline
+
- TC8: $R2 SHORT$           &  incorrect low pass filtering    &      &   SKLPIncorrect                    \\  
+ TC7:  R2 OPEN            &  No input signal                 &      &  SKLPnosignal                  \\ 
- TC9: $C1 OPEN$            &  reduced/incorrect low pass filtering         &      &  SKLPIncorrect\\ \hline
+ TC8:  R2 SHORT           &  incorrect low pass filtering    &      &   SKLPfilterIncorrect                    \\  \hline
- TC10: $C1 SHORT$          &  reduced/incorrect low pass filtering         &      &  SKLPIncorrect  \\  
+
- TC11: $C2 OPEN$           &  reduced/incorrect low pass filtering          &      & SKLPIncorrect   \\ \hline
+ TC9:  C1 OPEN             &  reduced/incorrect low pass filtering         &      &  SKLPfilterIncorrect\\ 
- TC12: $C2 SHORT$          &  No input signal, low signal                   &      &  SKLPnosignal \\  
+ TC10:  C1 SHORT           &  reduced/incorrect low pass filtering         &      &  SKLPfilterIncorrect  \\  \hline
+
+ TC11: C2 OPEN            &  reduced/incorrect low pass filtering          &      & SKLPfilterIncorrect   \\ 
+ TC12:  C2 SHORT           &  No input signal, low signal                   &      &  SKLPnosignal \\  \hline
                            \hline 
 \hline
 \end{tabular} 
-\label{tbl:firststage}
+\label{tbl:sallenkeylp}
 \end{table}
 
 We now can create a derived component to represent the Sallen Key low pass filter, which we can call $SKLP$.
@@ -593,29 +621,32 @@ $$ fm ( SKLP ) = \{ SKLPHigh,  SKLPLow, SKLPIncorrect, SKLPnosignal \} $$
 
 \paragraph{A failure mode model of Op-Amp Circuit 2.}
 
-We now have {\dcs} representing the three stages of this filter.
+We now have {\dcs} representing the three stages of this filter
-We   represent this as a block diagram to represent the signal flow, in figure~\ref{fig:blockdiagramcircuit2}.
+and this follows the signal flow in the filter circuit (see figure~\ref{fig:blockdiagramcircuit2}).
 
 
-\begin{figure}[h]
- \centering
- \includegraphics[width=400pt,keepaspectratio=true]{./blockdiagramcircuit2.png}
- % blockdiagramcircuit2.png: 689x83 pixel, 72dpi, 24.31x2.93 cm, bb=0 0 689 83
- \caption{Signal Flow though five pole low pass filter}
- \label{fig:blockdiagramcircuit2}
-\end{figure}
-
 
 
 As the signal has to pass though each block/stage
 in order to be `five~pole' filtered, we need to bring these three blocks together into a {\fg}
 in order to get a failure mode model for the whole circuit.
+We can index the Sallen Key stages, and these are marked on the ciruit schematic in figure~\ref{fig:circuit2002_FIVEPOLE}.
+
+\begin{figure}[h]+
+ \centering
+ \includegraphics[width=200pt]{./circuit2002_FIVEPOLE.png}
+ % circuit2002_FIVEPOLE.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331
+ \caption{Functional Groups in Five Pole Low Pass Filter on schematic}
+ \label{fig:circuit2002_FIVEPOLE}
+\end{figure}
+
+\pagebreak[4]
+
+So our final {\fg} will consist of the derived components $\{ LP1, SKLP_1, SKLP_2 \}$.
+We represent the desired FMMD hierarchy in figure~\ref{fig:circuit2h}.
 
 
-We can represent the desired FMMD hierarchy in figure~\ref{fig:circuit2h}.
+\begin{figure}[h]+
-
-
-\begin{figure}[h]
  \centering
  \includegraphics[width=300pt]{./circuit2h.png}
  % circuit2h.png: 676x603 pixel, 72dpi, 23.85x21.27 cm, bb=0 0 676 603
@@ -623,9 +654,82 @@ We can represent the desired FMMD hierarchy in figure~\ref{fig:circuit2h}.
  \label{fig:circuit2h}
 \end{figure}
 
+%\pagebreak[4]
+
+
+
+
+
+
+
+%$$ fm ( SKLP ) = \{ SKLPHigh,  SKLPLow, SKLPIncorrect, SKLPnosignal \} $$
+%$$ fm(LP1) = \{ LP1High,  LP1Low,  LP1ExtraLowPass, LP1NoLowPass \} $$
+
+\begin{table}[ht]+
+\caption{Five Pole Low Pass Filter: Failure Mode Effects Analysis: Single Faults} % title of Table
+\centering % used for centering table
+\begin{tabular}{||l|c|l|l|l||}
+\hline \hline
+ \textbf{Test} & \textbf{Circuit} & \textbf{  } & \textbf{General}   \\
+ \textbf{Case} &  \textbf{Effect}   & \textbf{  } & \textbf{Symptom Description}   \\
+%   R         &    wire        & res +         & res -    & description
+\hline
+\hline
+ TC1: $LP1$ LP1High         &      signal HIGH                  &       &   HIGH \\ 
+ TC2: $LP1$ SKLPLow         &      signal LOW                   &      &   LOW \\  
+ TC3: $LP1$ LP1filterIncorrect &    filtering incorrect            &         &  FilterIncorrect       \\   
+ TC4: $LP1$  LP1nosignal  &      no signal propogated             &      &   NO\_SIGNAL      \\ \hline
+
+
+
+ TC5: $SKLP_1$ High            &   signal HIGH             &      &   HIGH                  \\  
+ TC6: $SKLP_1$ Low             &   signal LOW                   &      &    LOW                  \\   
+ TC7:  $SKLP_1$ filterIncorrect      &   filtering incorrect              &      &    FilterIncorrect                  \\ 
+ TC8:  $SKLP_1$ nosignal       &  no signal propogated              &      &    NO\_SIGNAL                  \\  \hline
+
+ 
+ TC9: $SKLP_2$ High            &     signal HIGH                 &      &  HIGH                  \\  
+ TC10: $SKLP_2$ Low           &       signal LOW               &      &     LOW               \\  
+ TC11:  $SKLP_2$ filterIncorrect            &  filtering incorrect           &      &    FilterIncorrect                 \\ 
+ TC12:  $SKLP_2$ nosignal           &    no signal propogated          &      &     NO\_SIGNAL                  \\  \hline
+
+                           \hline 
+\hline
+\end{tabular} 
+\label{tbl:fivepole}
+\end{table}
+
+
+
+
+
+We now can create a {\dc} to represent the circuit in figure~\ref{fig:circuit2}, we can call it
+$FivePoleLP$ and applying the $fm$ function to it (see table~\ref{tbl:fivepole}) yields $fm(FivePoleLP) = \{ HIGH, LOW,  FilterIncorrect,  NO\_SIGNAL \}$.
+
+
+\pagebreak[4]
+
+The failure modes for the low pass filters are very similar, and the propogation of the signal
+is simple (as it is never inverted). The circuit under analysis is -- as shown in the block diagram (see figure~\ref{fig:blockdiagramcircuit2}) --
+three opamp driven non-inverting low pass filter elements; It is not suprising therefore that they have very similar failure modes.
+From a safety point of view, the failure modes $LOW$, $HIGH$ and $NO\_SIGNAL$
+could be easily detected; the failure symptom $FilterIncorrect$  may be less observable.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
 
-So out final {\fg} will consist of the derived components 
-$\{ LP1, SKLP_1, SKLP_2 \}$.
 
 \clearpage
 \section{Op-Amp circuit 3}
@@ -637,12 +741,9 @@ $\{ LP1, SKLP_1, SKLP_2 \}$.
 \caption{Circuit 3}
  \label{fig:circuit3}
 \end{figure}
-\end{tabular} 
-\label{ampfmea}
-\end{table}
 
-\clearpage
+%\clearpage
-\section{Standard Non-inverting OP AMP}
+%\section{Standard Non-inverting OP AMP}
 
 
 \clearpage
@@ -662,7 +763,7 @@ $\{ LP1, SKLP_1, SKLP_2 \}$.
 \paragraph{ Creating a fault hierarchy.}
 The main concept of FMMD is to build a hierarchy of failure behaviour from the {\bc}
 level up to the top, or system level, with analysis stages between each 
-transition to a higher level in the hierarchy. 
+transition to a higher level in the hierarchy. $$ fm(LP1) = \{ LP1High,  LP1Low,  LP1ExtraLowPass, LP1NoLowPass \} $$
 
 The first stage is to choose
 {\bcs} that interact and naturally form {\fgs}. The initial {\fgs} are   collections of base components.
@@ -846,7 +947,7 @@ they always have a small number of system failure modes.
 
 Idea stage on this section
 \begin{itemize}
- \item Look at OPAMP circuits
+ \item Look at OPAMP circuits, pick one (say $\mu$741)
  \item examine number of components and failure modes
  \item outline a proposed FMMD analysis
  \item Show FMD-91 OPAMP failure modes -- compare with FMMD